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arxiv: 2604.02433 · v1 · submitted 2026-04-02 · 🌌 astro-ph.CO · gr-qc

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· Lean Theorem

Cosmology-Independent Constraints on the Etherington Relation and SNeIa Absolute Magnitude Evolution from DESI-DR2

Sourav Das , Surhud More , Shadab Alam
Authors on Pith no claims yet

Pith reviewed 2026-05-13 20:16 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords Etherington relationdistance dualitySNe IaDESI-DR2supernova magnitude evolutionangular diameter distanceluminosity distancecosmology tests
0
0 comments X

The pith

DESI angular distances and supernova luminosities match the Etherington relation while bounding supernova magnitude evolution.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests whether luminosity distances measured from Type Ia supernovae and angular diameter distances measured by DESI follow the Etherington relation that links the two in any metric theory of gravity. The combined data sets show statistical agreement with the expected scaling of luminosity distance equaling angular diameter distance times (1 plus redshift) squared. This agreement supports photon number conservation and the metric nature of gravity while also showing that any additional redshift-dependent change in supernova absolute magnitude stays small.

Core claim

The measurements are statistically consistent with the Etherington relation. We interpret the absence of evidence of any deviation from this relation to constrain the evolution of the absolute magnitude of SNeIa to dM/dz = 0.07 ± 0.07 over and above the systematics that are already accounted for in the SNeIa analyses.

What carries the argument

The Etherington relation, which requires that luminosity distance equals angular diameter distance multiplied by (1 + z) squared.

If this is right

  • The data support photon number conservation and Lorentz invariance in metric gravity.
  • Supernova absolute magnitude shows little additional evolution with redshift beyond current corrections.
  • The relation supplies an extra consistency check that can reduce systematic uncertainties when geometric probes are used to study dynamical dark energy.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Higher-precision future surveys could tighten the bound on supernova magnitude evolution to test for subtle calibration drifts.
  • The same cross-check approach could be applied to other distance indicators such as gravitational-wave standard sirens without assuming a specific expansion history.
  • A clear future violation might indicate either unaccounted survey offsets or new physics affecting photon propagation.

Load-bearing premise

Any mismatch between the two distance indicators would be captured either by a violation of the Etherington relation or by the already-modeled SNeIa systematics.

What would settle it

A statistically significant deviation from the predicted ratio of luminosity distance to angular diameter distance at several redshifts in the DESI and supernova data sets.

Figures

Figures reproduced from arXiv: 2604.02433 by Shadab Alam, Sourav Das, Surhud More.

Figure 1
Figure 1. Figure 1: FIG. 1: The data points with errorbars in different panels show the distance modulus corresponding to SNeIa [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The validity of the Etherington relation as seen [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Cross-correlation matrix for [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Deviations from the Etherington relation from [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
read the original abstract

We carry out a test of the fundamental Etherington relation (cosmic distance duality relation) which relates the luminosity distance $D_{\rm L}$ and angular diameter distance $D_{\rm A}$ in metric theories of gravity. We use the latest measurements of the angular diameter distance as a function of redshift from the Dark Energy Spectroscopic Instrument Data Release 2 (DESI-DR2) and the luminosity distance from a variety of compilations of Supernovae of Type Ia (SNeIa). Our results indicate that these measurements are statistically consistent with the Etherington relation. In addition to providing a confirmation of the underlying assumptions of the Etherington relation, i.e., the metric nature of gravity, Lorentz invariance and photon number conservation, our results are also a stringent test of any residual systematic effects. We interpret the absence of evidence of any deviation from this relation to constrain the evolution of the absolute magnitude of SNeIa to $dM/dz = 0.07 \pm 0.07$ over and above the systematics that are already accounted for in the SNeIa analyses. We discuss how the Etherington relation can be used to constrain systematic parameters in the analyses of dynamical dark energy using geometric probes, to make it more robust against systematic effects.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript tests the Etherington relation (D_L = D_A (1+z)^2) by comparing angular-diameter distances from DESI-DR2 with luminosity distances from multiple SNeIa compilations. The authors report statistical consistency and interpret the result as a constraint on SNeIa absolute-magnitude evolution, dM/dz = 0.07 ± 0.07, above already-modeled systematics.

Significance. If the central consistency result holds after addressing calibration, the work supplies an independent check of metric gravity, photon conservation, and Lorentz invariance while furnishing a useful external bound on SNeIa systematics that can be folded into dynamical-dark-energy analyses.

major comments (2)
  1. [Method and results sections] The analysis combines DESI-DR2 angular-diameter distances with several SNeIa compilations yet does not introduce a nuisance parameter (or marginalize) over relative calibration offsets between the datasets. Because any constant or redshift-dependent zero-point offset enters directly into the D_L/D_A ratio, the quoted uncertainty on dM/dz may be underestimated; this is a load-bearing assumption for the derived bound.
  2. [Error budget discussion] The full covariance matrix, redshift-dependent selection cuts, and complete error budget for the combined likelihood are not presented in sufficient detail to verify that the reported consistency is robust against unmodeled cross-survey systematics.
minor comments (2)
  1. [Data section] Clarify the exact redshift overlap and binning scheme used when pairing DESI-DR2 and SNeIa data points.
  2. [Discussion] Add a brief statement on how the Etherington test can be propagated as a prior or consistency check in future BAO + SNeIa dark-energy fits.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major point below and have revised the manuscript to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: [Method and results sections] The analysis combines DESI-DR2 angular-diameter distances with several SNeIa compilations yet does not introduce a nuisance parameter (or marginalize) over relative calibration offsets between the datasets. Because any constant or redshift-dependent zero-point offset enters directly into the D_L/D_A ratio, the quoted uncertainty on dM/dz may be underestimated; this is a load-bearing assumption for the derived bound.

    Authors: We thank the referee for highlighting this issue. Constant calibration offsets between DESI-DR2 and the SNeIa compilations are absorbed into the absolute magnitude parameter M_0, which is marginalized when constraining the evolution dM/dz. To address possible redshift-dependent offsets, we will introduce an additional nuisance parameter for linear calibration evolution with redshift and marginalize over it in the likelihood. The revised manuscript will present the updated constraint on dM/dz with this marginalization included. revision: yes

  2. Referee: [Error budget discussion] The full covariance matrix, redshift-dependent selection cuts, and complete error budget for the combined likelihood are not presented in sufficient detail to verify that the reported consistency is robust against unmodeled cross-survey systematics.

    Authors: We agree that greater transparency in the error budget is important. In the revised manuscript we will add an appendix with the full covariance matrix of the combined likelihood. We will also expand the methods section to detail the redshift-dependent selection cuts and provide a complete breakdown of the error budget, including discussion of potential cross-survey systematics. These additions will enable verification of the robustness of the reported consistency. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper directly compares independent external measurements—angular diameter distances from DESI-DR2 and luminosity distances from multiple SNeIa compilations—against the Etherington relation D_L = D_A (1+z)^2. Statistical consistency is tested via this comparison, and the dM/dz = 0.07 ± 0.07 bound is presented as an interpretive consequence of the observed lack of deviation rather than any fitted parameter or self-referential definition. No steps in the provided text reduce by construction to the inputs, involve load-bearing self-citations, or smuggle ansatzes; the derivation remains self-contained against external data benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The analysis rests on the standard assumptions that underpin the Etherington relation plus the public distance catalogs; no new entities are introduced and only one parameter is constrained from the data.

free parameters (1)
  • dM/dz
    The linear evolution slope of SNeIa absolute magnitude is fitted to the observed distance residuals under the assumption that the Etherington relation holds exactly.
axioms (1)
  • domain assumption Gravity is metric, Lorentz invariance holds, and photon number is conserved
    These are the three physical assumptions the abstract states are tested by the Etherington relation.

pith-pipeline@v0.9.0 · 5535 in / 1392 out tokens · 71730 ms · 2026-05-13T20:16:57.967587+00:00 · methodology

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Reference graph

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